Tania Isbester has taken her fight to save her dog Izzy to the High Court of Australia in Canberra. Photo: Melissa Adams

The victim suffered a 1.5-centimetre laceration when she attempted to stop Izzy attacking another dog.

Izzy's owner, Tania Isbester, has appealed the death sentence to the highest court in the land, arguing one of the decision-makers had been biased against the dog after being involved in court proceedings for the attack.

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"It is too quick to then decide to destroy a dog that has been, by a professional, told is very human affectionate," Ms Isbester said.

"To destroy an animal or any living thing is not the first answer to be thought of. It's just inappropriate.

"We miss her greatly and think it's unjust that she's in this situation. It's unfair and irrational in the grand scheme of things."

In September 2013, Ms Isbester was put on a one-year community corrections order after pleading guilty in Ringwood Magistrates Court to 20 charges under the Domestic Animals Act.

Knox City Council then ordered Izzy be destroyed for the attack, ignoring an option to have the dog declared dangerous.

Ms Isbester unsuccessfully fought the decision through the Victorian justice system, arguing a member of the council's panel that decided Izzy's fate had been biased and had a conflict of interest as she had also brought the charges to court.

The matter came before the full court on Tuesday in what is understood to be the first time Australia's highest court has heard the case of a dog on death row.

Izzy's legal team asked the High Court to spare Izzy and order the council to pay costs.

Izzy's lawyer, Richard Kendall, QC, told the court the council officer had played an active role in both the court case and the decision to destroy the dog.

He argued the court case and panel decision were "inextricably linked", and the Appeal Court had erred in finding that because the criminal proceedings had ended, that the council employee had not been an accuser before council panel.

Mr Kendall said her role as a decision maker on the panel had constituted apprehended bias by way of a conflict of interest.

But Stephen Donaghue, QC, for Knox City Council, told the court the council officer had no interest in the decision that would cause her to be biased and had done "nothing more than her job".

When Justice Susan Kiefel asked if a fair minded observer believed the officer could make an impartial decision, Mr Donaghue argued the officer had not made the actual decision, just sat as part of a panel.